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A storm blows wind across the top of a roof at a speed of v = 26.3 m/s. Assume the air on the lower side of the roof (inside) is at rest and the roof is flat and has an area A = 38.9 m². The density of air is 1.28 kg/m³.1) What is the pressure differential across the top and bottom of the roof? 2) What is the net lift force on the roof due to the storm?

Respuesta :

Answer:

1)

442.7 Pa

2)

17221 N

Explanation:

1)

[tex]\rho[/tex] = density of air = 1.28 kg/m

[tex]v[/tex] = speed of wind at the top of rood = 26.3 m/s

[tex]\Delta P[/tex] = pressure difference across the top and bottom of the roof

Pressure difference across the top and bottom of the roof is given as

[tex]\Delta P = (0.5) \rho v^{2}[/tex]

inserting the values

[tex]\Delta P = (0.5) (1.28) (26.3)^{2}\\\Delta P = 442.7 Pa[/tex]

2)

[tex]F[/tex] = lift force

[tex]A[/tex] = area of the roof = 38.9 m²

[tex]\Delta P[/tex] = pressure difference across the top and bottom of the roof = 442.7 Pa

we know that

[tex]F = P A\\F = (442.7) (38.9)\\F = 17221 N[/tex]

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